SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samples

2025-12-18

AI Summary

In real-world scenarios, acquiring clean full-observation samples is prohibitively expensive, whereas noisy or partial observations are readily available. This paper addresses the problem of recovering the underlying data distribution from a black-box degradation process, given only a few clean samples and abundant noisy/sparse observations. We propose an EM-style iterative framework grounded in one-sided entropy-optimal transport and design a Stochastic Forward-Backward Deconvolution (SFBD) bridge model—a generalized bridge formulation that, for the first time, extends bridge modeling to arbitrary black-box degradations beyond Gaussian noise. We establish a theoretically grounded, verifiable criterion for distribution recoverability and introduce a test-time adaptive calibration mechanism. Extensive experiments across multiple benchmarks and heterogeneous measurement settings demonstrate consistent, state-of-the-art performance in PSNR, SSIM, and other metrics, validating the efficacy and robustness of few-shot guidance for large-scale distribution recovery.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Learning & Optimization for CV
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.

Problem

• Restores underlying distribution from abundant noisy samples using black-box corruption model.
• Determines recoverability under per-sample information loss with few clean samples.
• Generalizes SFBD to arbitrary measurement models beyond Gaussian corruption.

Innovation

• Bridge models map corrupted to ground-truth distributions
• Generalizes SFBD to arbitrary measurement models
• Uses one-sided entropic optimal transport and EM-like algorithm